Theorem on nonclassical states

Coherent Superpositions of Photon Creation Operations and Their Application to Multimode States of Light

We present a concise review of recent experimental results concerning the conditional implementation of coherent superpositions of single-photon additions onto distinct field modes. Such a basic operation is seen to give rise to a wealth of interesting and useful effects, from the generation of a tunable degree of entanglement to the birth of peculiar correlations in the photon numbers and the quadratures of multimode, multiphoton, states of light. The experimental investigation of these properties will have an impact both on fundamental studies concerning, for example, the quantumness and entanglement of macroscopic states, and for possible applications in the realm of quantum-enhanced technologies.

Photon added cat state: phase space structure and statistics

The phase space structure and statistics of the photon added cat state are studied in the state's general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke-Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.

Quantum State Engineering by Shortcuts to Adiabaticity in Interacting Spin-Boson Systems

We present a fast and robust framework to prepare nonclassical states of a bosonic mode exploiting a coherent exchange of excitations with a two-level system ruled by a Jaynes-Cummings interaction mechanism. Our protocol, which is built on shortcuts to adiabaticity, allows for the generation of arbitrary Fock states of the bosonic mode, as well as coherent quantum superpositions of a Schrödinger cat-like form. In addition, we show how to obtain a class of photon-shifted states where the vacuum population is removed, a result akin to photon addition, but displaying more nonclassicality than standard photon-added states. Owing to the ubiquity of the spin-boson interaction that we consider, our proposal is amenable for implementations in state-of-the-art experiments.

Quadrature Coherence Scale Driven Fast Decoherence of Bosonic Quantum Field States

We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a timescale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state's Wigner function. These two observations imply a large QCS constitutes a mark of "macroscopic coherence." Finally, we link the QCS to optical classicality: optical classical states have a small QCS and a large QCS implies strong optical nonclassicality.

Measuring Nonclassicality of Bosonic Field Quantum States via Operator Ordering Sensitivity

We introduce a new distance-based measure for the nonclassicality of the states of a bosonic field, which outperforms the existing such measures in several ways. We define for that purpose the operator ordering sensitivity of the state which evaluates the sensitivity to operator ordering of the Renyi entropy of its quasiprobabilities and which measures the oscillations in its Wigner function. Through a sharp control on the operator ordering sensitivity of classical states we obtain a precise geometric image of their location in the density matrix space allowing us to introduce a distance-based measure of nonclassicality. We analyze the link between this nonclassicality measure and a recently introduced quantum macroscopicity measure, showing how the two notions are distinct.

Thermal-difference states of light: true states of heralded photons

We introduce a three-parameter family of single-mode optical states whose density operator is a weighted difference of two thermal states, the thermal-difference states. We identify the parameter values for which these states have a negative non-singular P-function, implying they are nonclassical. We show that the states of the “heralded photons” generated via spontaneous parametric downconversion belong to this family, with the three parameters corresponding to the nonlinear gain and the losses in the signal and the idler channels. The thermal-difference states yield new benchmark states for the analysis of nonclassicality and quantum macroscopicity criteria.

Deterministic nonclassicality from thermal states

Coupling an oscillator to a single two-level system is one of the most fundamental interactions in quantum physics. We report on a dynamical effect during which a thermal state of an oscillator is unconditionally transformed to a highly nonclassical state with negative Wigner function values by mere absorbtion by a single uncontrolled two-level system. This complements the traditional test of Rabi oscillations and it serves as a simply measurable witness that the process in question is highly nonclassical. The process is experimentally feasible with possible experimental implementation in a number of experimental platforms with intrinsic Jaynes-Cummings interaction and it has the potential of enabling deterministic generation of nonclassical quantum states.

Nonclassical light revealed by the joint statistics of simultaneous measurements

Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.

Scheme for proving the bosonic commutation relation using single-photon interference

We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.

Probing quantum commutation rules by addition and subtraction of single photons to/from a light field

The possibility of arbitrarily "adding" and "subtracting" single photons to and from a light field may give access to a complete engineering of quantum states and to fundamental quantum phenomena. We experimentally implemented simple alternated sequences of photon creation and annihilation on a thermal field and used quantum tomography to verify the peculiar character of the resulting light states. In particular, as the final states depend on the order in which the two actions are performed, we directly observed the noncommutativity of the creation and annihilation operators, one of the cardinal concepts of quantum mechanics, at the basis of the quantum behavior of light. These results represent a step toward the full quantum control of a field and may provide new resources for quantum information protocols.

Quantum state reconstruction of the single-photon Fock state

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.